# Is f(x)=3x^-2 -3 a function?

We can rewrite $f \left(x\right)$ as $f \left(x\right) = \frac{3}{x} ^ 2 - 3$. For this equation to be a function, one value of $x$ must not give more than one value for $y$, so each $x$ value has a unique $y$ value. Also, every value for $x$ must have a value for $y$.
In this case, each value for $x$ has one value for $y$. However, $x \ne 0$ since $f \left(0\right) = \frac{3}{0} - 3 = \text{undefined}$.
So, $f \left(x\right)$ is not a function.
However, it can be made a function by applying limits or ranges of $x$ values, in this case it is a function if $f \left(x\right) = 3 {x}^{-} 2 - 3 , x \ne 0$.